Global solutions and blowing-up solutions for a nonautonomous and nonlocal in space reaction-diffusion system with Dirichlet boundary conditions

2020 ◽  
Vol 23 (4) ◽  
pp. 1025-1053
Author(s):  
Marcos J. Ceballos-Lira ◽  
Aroldo Pérez
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Coupled System ◽  
Dirichlet Boundary Conditions ◽  
Weakly Coupled System ◽  
Blowing Up ◽  
Fractional Diffusions

AbstractWe give sufficient conditions for global existence and finite time blow up of positive solutions for a nonautonomous weakly coupled system with distinct fractional diffusions and Dirichlet boundary conditions. Our approach is based on the intrinsic ultracontractivity property of the semigroups associated to distinct fractional diffusions and the study of blow up of a particular system of nonautonomus delay differential equations.

scholarly journals Multiple solutions of fourth-order difference equations with different boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yuhua Long ◽  
Shaohong Wang ◽  
Jiali Chen
Keyword(s):  
Boundary Conditions ◽  
Fourth Order ◽  
Difference Equations ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Sufficient Conditions ◽  
Dirichlet Boundary Conditions ◽  
Invariant Sets ◽  
Mountain Pass Lemma ◽  
Order Difference

Abstract In the present paper, a class of fourth-order nonlinear difference equations with Dirichlet boundary conditions or periodic boundary conditions are considered. Based on the invariant sets of descending flow in combination with the mountain pass lemma, we establish a series of sufficient conditions on the existence of multiple solutions for these boundary value problems. In addition, some examples are provided to demonstrate the applicability of our results.

scholarly journals The nonlocal mean-field equation on an interval

2019 ◽  
Vol 22 (05) ◽  
pp. 1950028
Author(s):  
Azahara DelaTorre ◽  
Ali Hyder ◽  
Luca Martinazzi ◽  
Yannick Sire
Keyword(s):  
Field Equation ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mean Field ◽  
Higher Order ◽  
Dirichlet Boundary Conditions ◽  
Field Equations ◽  
Mean Field Equations ◽  
Blowing Up ◽  
Mean Field Equation

We consider the fractional mean-field equation on the interval [Formula: see text] [Formula: see text] subject to Dirichlet boundary conditions, and prove that existence holds if and only if [Formula: see text]. This requires the study of blowing-up sequences of solutions. We provide a series of tools in particular which can be used (and extended) to higher-order mean field equations of nonlocal type.

scholarly journals Blow-Up of Solutions with High Energies of a Coupled System of Hyperbolic Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Jorge A. Esquivel-Avila
Keyword(s):  
Initial Data ◽  
Blow Up ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
Coupled System ◽  
Initial Energy ◽  
Evolution System ◽  
High Energies ◽  
Second Order In Time

We consider an abstract coupled evolution system of second order in time. For any positive value of the initial energy, in particular for high energies, we give sufficient conditions on the initial data to conclude nonexistence of global solutions. We compare our results with those in the literature and show how we improve them.

Sign in / Sign up

Export Citation Format

Share Document